Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators
نویسندگان
چکیده
This paper studies the asymptotic properties of partitioning estimators of the conditional expectation function and its derivatives. Mean-square and uniform convergence rates are established and shown to be optimal under simple and intuitive conditions. The uniform rate explicitly accounts for the effect of moment assumptions, which is useful in semiparametric inference. A general asymptotic integrated mean-square error approximation is obtained and used to derive an optimal plug-in tuning parameter selector. A uniform Bahadur representation is developed for linear functionals of the estimator. Using this representation, asymptotic normality is established, along with consistency of a standard-error estimator. The finite-sample performance of the partitioning estimator is examined and compared to other nonparametric techniques in an extensive simulation study.
منابع مشابه
Part II Supplement for “Optimal Convergence Rates, Bahadur Representation, and Asymptotic Normality of Partitioning Estimators”
Abstract This is a supplemental appendix for “Optimal Convergence Rates, Bahadur Representation, and Asymptotic Normality of Partitioning Estimators”. We first present detailed proofs of all the theoretical results from the main text. Lemmas and other claims are restated before proof, and as such this section may replace the appendix contained in the main manuscript. Note that equation numbers ...
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